Interactive volume segmentation with differential image foresting transforms

The absence of object information very often asks for considerable human assistance in medical image segmentation. Many interactive two-dimensional and three-dimensional (3-D) segmentation methods have been proposed, but their response time to user´s actions should be considerably reduced to make them viable from the practical point of view. We circumvent this problem in the framework of the image foresting transform (IFT)-a general tool for the design of image operators based on connectivity-by introducing a new algorithm (DIFT) to compute sequences of IFTs in a differential way. We instantiate the DIFT algorithm for watershed-based and fuzzy-connected segmentations under two paradigms (single-object and multiple-object) and evaluate the efficiency gains of both approaches with respect to their linear-time implementation based on the nondifferential IFT. We show that the DIFT algorithm provides efficiency gains from 10 to 17, reducing the user´s waiting time for segmentation with 3-D visualization on a common PC from 19-36 s to 2-3 s. We also show that the multiple-object approach is more efficient than the single-object paradigm for both segmentation methods.